A few remarks on boundedness in topological modules and topological\n groups

2016/11/05 by Omid Zabeti, Zabeti, Omid
Decision Sciences · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Fuzzy and Soft Set Theory #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1611.01631

openalex publication_date 2016/11/05 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

Let X, Y, and Z be topological modules over a topological ring R. In the\nfirst part of the paper, we introduce three different classes of bounded\nbigroup homomorphisms from X\× Y into Z with respect to the three\ndifferent uniform convergence topologies. We show that these spaces form again\ntopological modules over R. In the second part, we characterize bounded sets\nin the arbitrary product of topological groups with respect to the both product\nand box topologies.\n

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